Graph Theory Quiz

What is a vertex in a graph?

• A line segment connecting two points

• A dot representing a point in the graph

• A loop within the graph

• A subset of edges

What is an edge in a graph?

• A dot representing a point

• A set of vertices

• A line segment connecting vertices

• A table of connections

What is the degree of a vertex?

• The number of edges in the graph

• The number of edges incident on the vertex

• The number of vertices connected to a loop

• The total number of isolated vertices

What do you call an edge that connects a vertex to itself?

• Parallel edge

• Isolated edge

• Loop

• Adjacent edge

Which type of graph has no loops or parallel edges?

• Directed graph

• Complete graph

• Simple graph

• Bipartite graph

Which of the following statements correctly describes a complete graph?

• It contains vertices that are not connected.

• All pairs of vertices are connected by edges.

• It has loops at every vertex.

• It is a bipartite graph with no edges.

How is a directed graph different from an undirected graph?

• It has loops at all vertices.

• It has an associated direction for each edge.

• It has no isolated vertices.

• It is a complete graph by default.

Why is the Handshake Theorem valid for graphs without loops?

• It counts each edge once, irrespective of direction.

• Each edge is shared between two vertices, doubling the total.

• It only applies to complete graphs.

• Loops are excluded to simplify the calculation.

If a vertex vvv is isolated, what is its degree?

• 0

• 1

• 2

• Undefined

What is the difference between parallel edges and a loop?

• Parallel edges connect the same two vertices, while a loop connects a vertex to itself.

• Parallel edges connect different vertices, while a loop connects two graphs.

• Both are the same in a simple graph.

• Parallel edges form a cycle, while loops do not.